REVIEW 30 cited by
Anyons in an exactly solved model and beyond
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
A spin 1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static $\mathbb{Z}_{2}$ gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number $\nu$. The Abelian and non-Abelian phases of the original model correspond to $\nu=0$ and $\nu=\pm 1$, respectively. The anyonic properties of excitation depend on $\nu\bmod 16$, whereas $\nu$ itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.
Forward citations
Cited by 30 Pith papers
-
Universal framework with exponential speedup for the quantum simulation of quantum field theories including QCD
Fermion extensions of the orbifold-lattice simulation framework achieve O(L^d) gates per Trotter step for QCD-like theories without oracles.
-
Non-Invertible Anyon Condensation and Level-Rank Dualities
New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
-
Decoupling 2D translation-invariant topological CSS codes
Every 2D translation-invariant topological CSS code is local-unitarily equivalent, at the maximal anyon-preserving translation symmetry, to stacks of toric codes and product states, with an explicit polynomial-time co...
-
Approximate Quantum Error Correction at Chiral Topological Edges
Chiral edge codes have local-erasure robustness governed by power-law exponents with hierarchy γ≥α≥min{α,β}, so the 2D code is at least as robust as its 1D CFT reduction.
-
Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies
An order-five Sp(4,Z) duality acts projectively on 3d U(1)^2 theories, and its hierarchy operations generate candidate bilayer quantum Hall states at 3/8+3/8 and 5/12+5/12.
-
Entanglement fingerprint of a non-invertible symmetry: exact Fibonacci cut charges on the lattice
Even-length antiferromagnetic ground state of the critical golden chain carries exact Fibonacci cut-charge weights P_tau/P_1=phi^2 and boundary entropy log g=log phi for the duality defect.
-
Monopoles, Center Vortices, Confinement in (3+1)d, and the Lens-Space Twisted Partition Function
Proposes torus and lens-space twisted partition functions as criteria for center-vortex and monopole condensation and proves vortex condensation implies monopole condensation in gapped phases.
-
Infinite-Order Lattice Chiral Anomalies and CPT
Lattice CPT symmetry upgrades the Onsager chiral symmetry anomaly from order two to infinite order, better matching the continuum chiral anomaly, with discussion of associated 2+1d SPT phases.
-
Hypergroup Symmetry in Relative Quantum Field Theories and Chiral Algebras
Framework for hypergroup symmetries in relative QFTs establishes one-to-one correspondence between finite symmetries and finite-index conformal embeddings in rational chiral algebras, with implications for gluing left...
-
Topological lattice gauge theory enriched by non-invertible symmetry
Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
-
Gauging Non-Invertible Symmetries in (2+1)d Topological Orders
A framework for gauging non-invertible symmetries in (2+1)d TQFTs, unifying 0-form and 1-form gauging via surface algebras, with constraints and toric-code examples.
-
QG from SymQRG: AdS$_3$/CFT$_2$ Correspondence as Topological Symmetry-Preserving Quantum RG Flow
A framework called SymQRG identifies 3D quantum gravity as the symmetry-preserving RG flow of 2D CFTs, realized discretely by U_q(SL(2,R)) 6j symbols.
-
Higher Gauging and Non-invertible Condensation Defects
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
-
Orthonormal bases for higher Hilbert spaces
For finite-dimensional 3-Hilbert spaces, orthonormal bases exist uniquely up to contractible choice, and the Yoneda embedding into the presheaf 3-Hilbert space is an isometric equivalence.
-
The state/defect correspondence
Establishes a one-to-one correspondence between states and p-dimensional defects in higher-form Maxwell theories via an extended Kac-Moody algebra generated by conserved charges from mixed anomalies, mapping dressed W...
-
Notes on (-2)-form symmetries
Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, an...
-
Magnetic fields in monoclinic $\alpha$-RuCl$_3$ reveal rhombohedral inclusions underlying apparent oscillations
Apparent quantum spin liquid signatures in α-RuCl₃ under in-plane fields arise from multiple shifted AFM phase boundaries due to rhombohedral inclusions in monoclinic samples.
-
Exactly Solvable Topological Phase Transition in a Quantum Dimer Model
A tunable triangular-lattice quantum dimer model is shown to undergo an exactly solvable continuous topological phase transition at edge weight α = 3, from a Z2 quantum spin liquid to a columnar ordered state.
-
From gauging to duality in one-dimensional quantum lattice models
Gauging and duality transformations are equivalent up to constant depth quantum circuits in one-dimensional quantum lattice models, demonstrated via matrix product operators.
-
SymTFT actions, Condensable algebras and Categorical anomaly resolutions
For Q8 and Rep(Q8), the paper computes condensable algebras, identifies intrinsically gapless SPT phases, and derives fusion-category short exact sequences that resolve categorical anomalies.
-
Statistics in 3d gravity from knots and links
Fragmentation of knots and links by Wilson lines builds wormhole amplitudes that give non-perturbative Gaussian and non-Gaussian corrections to OPE statistics in 3d gravity and CFT2.
-
Quasiparticle tunnelling in two coupled chiral SYK model
Two weakly coupled chiral SYK models in 1+1 dimensions stay gapless and show massless collective tunneling modes, with no temperature-dependent free-energy correction at leading order.
-
On the Physics of Higher Condensation Defects
Topological defects from higher gauging are shown, via explicit Lagrangian computations, to satisfy the Karoubi completeness condition of Johnson-Freyd's higher fusion categories, and this is identified with splitting...
-
The $S=\frac{1}{2}$ XY and XYZ models on the two or higher dimensional hypercubic lattice do not possess nontrivial local conserved quantities
The S=1/2 XY and XYZ models on d≥2 hypercubic lattices possess no nontrivial local conserved quantities.
-
Operational Tube-Sector Theory of Quantum State Distinguishability Under Generalized Symmetries
Introduces tube-sector probabilities from the center of boundary tube algebras to give optimal one-shot distinguishability of quantum states under generalized symmetries.
-
Extending fusion rules with finite subgroups: A general construction of $Z_{N}$ extended conformal field theories and their orbifoldings
Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
-
Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
-
Absence of nontrivial local conserved quantities in the quantum compass model on the square lattice
The quantum compass model on the square lattice possesses no nontrivial local conserved quantities besides the Hamiltonian.
-
Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
New classes of boundary and coupled conformal field theories are constructed from Z_N gauging, with a proposed dictionary to topological order, nonchiral anyons, and domain walls.
-
Les Houches Lecture Notes on Tensor Networks
A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.
Discussion (0). Continue with ORCID to comment.